Adding and Subtracting Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.

Front

How do you add rational expressions with the same denominator?

Back

To add rational expressions with the same denominator, combine the numerators and keep the denominator the same.

Front

How do you subtract rational expressions with the same denominator?

Back

To subtract rational expressions with the same denominator, subtract the numerators and keep the denominator the same.

Front

What is the first step in adding rational expressions with different denominators?

Back

The first step is to find a common denominator.

Front

How do you find a common denominator for two rational expressions?

Back

The common denominator is the least common multiple (LCM) of the denominators.

Front

What is the process of simplifying a rational expression?

Back

To simplify a rational expression, factor the numerator and denominator and then cancel any common factors.

Front

What does it mean to 'cancel' in rational expressions?

Back

Canceling means removing common factors from the numerator and denominator.

Front

What is the importance of checking for restrictions in rational expressions?

Back

Restrictions are important because they indicate values that make the denominator zero, which are not allowed.

Front

What is an example of a restriction in the expression 1/(x-3)?

Back

The restriction is x ≠ 3, since it would make the denominator zero.

Front

How do you add the rational expressions 1/(x+2) + 1/(x-2)?

Back

Find a common denominator, which is (x+2)(x-2), then rewrite each fraction and combine.